1.x sin x

Find the general solutions of the following differential equations. x sin x dy/dx+(x cos x+sin x)y=sin x

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

Prove that (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x) = 2 tan x

int(e^(x)sin x+cot x+x sin x)/(sin x)dx

The number of distinct real roots of the equation, |(cos x, sin x , sin x ),(sin x , cos x , sin x),(sinx , sin x , cos x )|=0 in the interval [-pi/4,pi/4] is :

(cos 2x sin x + cos 6x sin 3x)/(sin 2x sin x + sin 6x sin 3x) =cot 5x

e ^ (x) sin x tan x + e ^ (x) sin x + e ^ (x) sin x sec ^ (2) x

int (cos x-sin x) / ((cos x + sin x) dx)

int ((cos x + sin x) / (cos x-sin x)) dx